A dancing-master, so called from his kit or cittern, a small fiddle, which dancing-masters always carry about with them, to play to their scholars. The kit is likewise the whole of a soldier’s necessaries, the contents of his knapsack: and is used also to express the whole of different commodities: as, Here, take the whole kit; i.e. take all.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Kissing Crust * Kit-cat ClubNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes